I m confused between computational finance, financial engineering, risk analysis, quant finance and quantitative economics??
Excluding risk analysis, in some ways these are all the same. (Yes. That's a generalization). What you should do is do a cursory search/review of each area, to find the overlaps. Taking a deeper look into the overlapping areas could be of interest to you in the short-term. Later on, you will decide what you do/don't like. Then you can switch you focus.
For example, just google direct questions like "How is risk analysis used in financial engineering?"
I'd also suggest looking up 2-3 Masters Degree programs on those topics, and comparing the syllabus. After removing the basic classes, you will see which of the intermediate and advanced classes are shared.
Here is my own opinion of what you'd encounter in classes or programs with those names:
1. Computational Finance - use
Python to price options, and do credit valuations. Implement, Binomial Options Model, Black Scholes Model, Stochastic price path model, Fonte Carlo sim, Fourier and Fast Fourier for pricing, Interest Rate stochastic models, all in
Python, to get outputs of: single values, distribution graphs, sample path graphs, curvatures/rate of changes at points, intervals.
2. Financial Engineering - the "field" of study that includes every other term you listed. In particular, you must learn Stochastic Calculus.
If Financial Engineering were just one class, it would be the same as the Computational Finance class.
3. Risk Analysis - risk has many areas. When it comes to financial instruments (and such), risk is measured with words like "volatility" and concepts like standard deviation. Therefore, you will explore financial applications of standard dev, like Value-at-Risk, or Bond pricing with convexity, or special stochastic models of volatility (Vasicek, Hull-White, etc). You can plug stochastic volatility models into pricing models which tend to use/assume constant volatility (e.g. Black Scholes)
4. Quantitative Finance - the cooler name of Financial Engineering. In terms of Master's programs, a Masters in FinEng and a Masters in QuantFin, will cover almost exactly the same thing. However, QuantFin can be a bit more broad.
5. Quantitative Economics - basically economics with more math and less strange notation. For example, Econometrics - the combination of time-series modeling with economic concepts that govern the path of the time-series holistically. For example, a "stylized-fact" of Financial time-series is that their returns tend to have zero mean. This is not necessarily the case for time-series in general, and thus this "rule" is fro the Economic theory side of things.
Use anything but Investopedia to get a better definition of any of your terms, or those that I mentioned.
